The coastline paradox
Greenland is the largest island in the world. Its rugged coastline is also one of the longest in the world at an estimated length of roughly the same as the circumference of the Earth at the Equator. It’s estimated, because coastlines are difficult things to measure.
The coastline paradox, also known as the Richardson Effect after the mathematician Lewis Fry Richardson, describes this measurement difficulty. Richardson’s interest in the problem was sparked by Portugal and Spain claiming different lengths to border between the two countries. As Richardson looked into it he realised that the Portuguese and the Spanish were using different length rulers. When they measured the irregularly-shaped borderline by counting how many increments of the ruler it was, they got different answers.
Wherever the thing being measured has an irregular shape, the measurement will always depend on the size of the measure.
If you were feeling ambitious and set out to measure the length of the coast of Greenland, you might take a kilometre-long measuring stick with you. You’d start somewhere on the coast, perhaps Cape Farewell, Greenland’s most southerly point, and you’d lay your measuring stick along the coast. Then you’d move the stick, end over end, counting as you go until you get all the way around the coast and back round to Cape Farewell. You’d probably end up with a measurement somewhere around 39,330 kilometres.
If you did the same exercise again, but this time with a metre long measuring stick you’d get into all the rough ins and outs that your kilometre-long measuring stick smoothed out. So, when you got back round to where you’d started you’d have a much longer measurement of the same coastline.
If you went back yet again, this time with a centimetre long measuring stick, you’d get into even smaller twists and turns of the rocks and ice, and so get an even longer measurement of the same coastline.
Fry realised that there was a “mathematical uncertainty in the measurement of irregular boundaries”, and said that as the measuring stick approaches zero the length of the coastline approaches infinity.
What if, instead of spending your time measuring Greenland, you had some other large goal you wanted to achieve? If your goal doesn’t have an exact definition, and what big goal ever does, then it’s a bit like the Greenland coastline, or the Portugal-Spain border - it’s irregularly shaped. To measure your progress towards achieving a goal like that you might breakdown the things you need to do into small, achievable tasks. Ticking them off shows you how many you’ve completed on your way towards the goal.
This approach to achieving goals is sometimes called ‘think big, start small’. It encourages us to have ambitious goals with the promise that if we complete enough small steps towards them, then one day we’ll get there, we’ll achieve our goals. For irregularly-shaped, uncertain goals, that might not work.
The coastline paradox shows us the inherent contradiction of the ‘think big, start small’ mantra; the smaller your steps, the further away the big goal becomes. Starting with small specific actions doesn’t guarantee achieving big irregular-shaped, uncertain goals, because how you define and measure those steps changes what you end up with.
Muhammad Yunus, the Bangladeshi social entrepreneur and civil society leader, suggests that instead of thinking big we just start. Start with whatever is in front of you, something you can do now. He didn’t start with the big goal of being awarded a Nobel Peace Prize. He started by providing microfinance loans to entrepreneurs too poor to qualify for traditional bank loans, and founding the Grameen Bank, and helping people find ways to break out of poverty. And then he was awarded the Nobel Peace Prize.
If we set out with the one big goal to get an even more accurate measure of the coast of Greenland we might miss all the other things we could have achieved along the way.